85 (number)

85 (eighty-five) is the natural number following 84 and preceding 86.

← 84 85 86 →
← 80 81 82 83 84 85 86 87 88 89 → List of numbers Integers ← 0 10 20 30 40 50 60 70 80 90 →
Cardinal	eighty-five
Ordinal	85th (eighty-fifth)
Factorization	5 × 17
Divisors	1, 5, 17, 85
Greek numeral	ΠΕ´
Roman numeral	LXXXV, lxxxv
Binary	10101012
Ternary	100113
Senary	2216
Octal	1258
Duodecimal	7112
Hexadecimal	5516

In mathematics

85 is:

• the product of two prime numbers (5 and 17), and is therefore a semiprime of the form (5.q) where q is prime.
• specifically, the 24th Semiprime, it being the fourth of the form (5.q).
• together with 86 and 87, forms the second cluster of three consecutive semiprimes; the first comprising 33, 34, 35. ^[1]
• with a prime aliquot sum of 23 in the short aliquot sequence (85,23,1,0).
• an octahedral number. ^[2]
• a centered triangular number. ^[3]
• a centered square number. ^[4]
• a decagonal number. ^[5]
• the smallest number that can be expressed as a sum of two squares, with all squares greater than 1, in two ways, 85 = 9² + 2² = 7² + 6². ^[6]
• the length of the hypotenuse of four Pythagorean triangles.
• a Smith number in decimal. ^[7]

In other fields

• The radix of the Ascii85 (sometimes called Base85) binary-to-text encoding
• Part of the assignation for the Toyota AE85, commonly referred to as an "eight-five".

References

1. Sloane, N. J. A. (ed.). "SequenceA056809(Numbers k such that k, k+1 and k+2 are products of two primes)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
2. Sloane, N. J. A. (ed.). "SequenceA005900(Octahedral numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
3. Sloane, N. J. A. (ed.). "SequenceA005448(Centered triangular numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
4. Sloane, N. J. A. (ed.). "SequenceA001844(Centered square numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
5. Sloane, N. J. A. (ed.). "SequenceA001107(10-gonal (or decagonal) numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.
6. Sloane, N. J. A. (ed.). "SequenceA007692(Numbers that are the sum of 2 non-zero squares in 2 or more ways)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.. The two smaller numbers on this list, 50 and 65, have 1 as one of the squares in their representations as sums of two squares.
7. Sloane, N. J. A. (ed.). "SequenceA006753(Smith numbers)". The On-Line Encyclopedia of Integer Sequences . OEIS Foundation.

External links

• 85
• Jorge Stolfi, The Hollywood Constant.